Commitment schemes are arguably among the most important and
useful primitives in cryptography. According to the computational
power of receivers, commitments can be classified into three
possible types: {\it computational hiding commitments,
statistically hiding commitments} and {\it perfect computational
commitments}. The fist commitment with constant rounds had been
constructed from any one-way functions in last centuries, and the
second with non-constant rounds were constructed from any one-way
functions in FOCS2006, STOC2006 and STOC2007 respectively,
furthermore, the lower bound of round complexity of statistically
hiding commitments has been proven to be $\frac{n}{logn}$ rounds
under the existence of one-way function.
Perfectly hiding commitments implies statistically hiding, hence,
it is also infeasible to construct a practically perfectly hiding
commitments with constant rounds under the existence of one-way
function. In order to construct a perfectly hiding commitments
with constant rounds, we have to relax the assumption that one-way
functions exist. In this paper, we will construct a practically
perfectly hiding commitment with two-round from any one-way
permutation. To the best of our knowledge, these are the best
results so far.